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periodic B.C.

ChangyongCao's picture

Dear ALL,

I am currently want to code a little program for micromechanics analysis based on FEM. But I am not sure how to implement the periodic B.C. in it.  I refer the general formulations of FEM for engineers not the tensor forms. Hope you give a detailed explanation or example. Thanks very much.


Charson Y.S.


Stephan Rudykh's picture

Dear Charson,

 If your goal is to impose a strictly periodic BC you just relate the displacement of the nodes on opposite bounaries (edges, phases...). Like this

u(left)= u(right) + deformation.

 You may have to prescribe the BC for each node or only for boundaries depending on FEM you use. You may want to check out this paper

Especially, its part Finite Element Simulations . There are some usefull details on periodic boundary conditions.


Good luck!



Wenbin Yu's picture

If you formulate the problem in terms of fluctuating functions, then you can simply let the functions equal to each other on the periodic boundaries. In the FEM implementation, the nodes on one edge are thus slave to the nodes on corresponding edges. That is how VAMUCH is formulated and implemented.This way, you actually do not have to worry about periodic BCs and corresponding applied loads.

ChangyongCao's picture

Dear Prof. Yu,

Thank you for your suggestion. One question arised is how to apply the controled strains/B.C. for micro analysis when implement it?

Best regards,

Charson Y.S. CAO

Wenbin Yu's picture


The beauty is that you don't have to apply controlled strains/BC if you use VAMUCH or follow a fomulation similar to it. Note these controlled strains are arbitrary and will not affect the results, as far as linear theory concerned.


ChangyongCao's picture

Hi, Prof. Yu,

I have done for 2D because it is easy to get it opposite nodes after meshing. However, I have no idea for 3D problems. It has so many irreglar ones so that it is diffult or cannot find the opposite nodes in the other surface. How to deal with this problem in code? Any comment/suggestion is welcome and appreciated.Thank you.

Charson CAO

Wenbin Yu's picture

In a mesh generator, you mesh the surfaces first to make sure they have corresponding nodes. In fact if you use VAMUCH-ANSYS interface, you don't have to worry about this. The macro will automatically generate the right mesh for you and then use VAMUCH to calculate the effective properties.

ChangyongCao's picture

Hi, Stephan,

Do you have any experience in 3D micro simulation?

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